Valuation of exotic options under shortselling constraints
type: Item
instance of: scholarly article
title: Valuation of exotic options under shortselling constraints
zbMATH Open document ID: 1002.91021
author: Uwe Schmock
author: Steven Shreve
author: Uwe Wystup
published in: Finance and Stochastics
publication date: 2002-12-01T00:00:00Z
review text: This article deals with the valuation of options with discontinuous payoffs. The authors use a method based on the idea of super-replication. The price of a contingent claim obtained by this method is called the upper hedging price. Let \((\Omega,{\mathcal F}(T),P)\) be a canonical probability space for a Brownian motion \(W(t)\), and let \(F(t), 0\leq t\leq T\) be the corresponding filtration. Let us denote by \(\Lambda=\{\lambda: \lambda\) is an \(\{F(t),0\leq t\leq T\}\)-adapted, nondecreasing, continuous process with \(\lambda(0)=0\}\). The following result is proved. Let \(g\) be a nonnegative lower semicontinuous function defined on \(C_{+}[0,T]\) - the space of nonnegative continuous functions on \([0,T]\). The upper hedging price for the contingent claim with payoff \(g(S)\) at the expiration date \(T\) and hedge-portfolio constraint \(\pi(t)\geq -\alpha, 0\leq t\leq T, \alpha\in [0,\infty)\) a.s. is \(v(0, S(0);\alpha)=\sup_{\lambda\in\Lambda} E\left[e^{-rT- \alpha\lambda(T)}g(Se^{-\lambda})\right]\), where \(S=\{S(t)= S(0)\exp\{\sigma W(t)+rt-\sigma^2 t/2\}, 0\leq t\leq T\}\). An application of this result for valuation of the knock-out call option is presented as well as an extension of the obtained result for the knock-out options with discrete checking of barriers. As examples the cactus option, digital put, discrete barrier option, vanilla put, lookback put, Asian put, book of two barrier options are considered.
Mathematics Subject Classification ID: 91G20
zbMATH DE Number: 1837543
zbMATH Keywords: exotic options
zbMATH Keywords: shortselling constraints
zbMATH Keywords: super-replication
zbMATH Keywords: upper hedging price
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
full work available at URL: s007800100050
OpenAlex ID: W2128350654
DOI: 10.1007/S007800100050
description: scientific article; zbMATH DE number 1837543